Prove That Under the Extended Least Squares Assumptions the OLS $\hat { \beta}$

question 38

Essay

Prove that under the extended least squares assumptions the OLS estimator $\hat { \beta}$ is unbiased and that its variance-covariance matrix is $\sigma _ { u } ^ { 2 }$ (X'X)^-1.

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Definitions:

Nonrefundable Ticket

A type of ticket purchase that cannot be returned for a refund. These tickets generally offer a cost advantage but less flexibility.

Wear and Tear

The damage or deterioration resulting from ordinary use over time.

MC Curves

also known as Marginal Cost Curves, represent the additional cost incurred in producing one more unit of a good or service.

AVC Curves

The Average Variable Cost curve shows how the average variable cost of production changes as the output level changes.